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Stationary properties of a Brownian gyrator with non-Markovian baths

We investigate the stochastic behavior of a two-temperature Langevin system with non-Markovian thermal reservoirs. The model describes an overdamped Brownian particle in a quadratic potential and coupled to heat baths at different temperatures. The reservoirs are characterized by Gaussian white and colored noises and a dissipation memory kernel. The stationary states present non-trivial average rotational motion influenced by stochastic torques due to harmonic, friction and fluctuating thermal forces. However, the Markovian limit leads to a vanishing average torque produced by fluctuating thermal forces. We also study the effects of memory on the stochastic heat and the entropy production in the steady-state regime.